
The coefficient function \(a: \mathbb {N}\rightarrow \mathbb {C}\)  is said to define a multiplicative character [1]}. The convergence
of the series also puts a bound on the growth of the coefficients, which for a cusp form is \(|a(p)| \le Cp^{{(k-1)}/{2}}\)  for \(C\)  of order 1. Due to
the above properties of its coefficients, the \(L\) -function of a cusp form \(f\)  ModularL too admit an Euler product form
\(L(s,f) = \sum _{n=1}^\infty \frac{a(n)}{n^s} = \prod _{p\,\in \,{\mathrm {primes}}} \frac{1}{\left(1 - a(p) p^{-s} +\chi (p)p^{k-1} p^{-2s}\right)} \) 
